compute the nullspace of a Matrix - Maple Help

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LinearAlgebra[Generic][NullSpace] - compute the nullspace of a Matrix

Calling Sequence

NullSpace[F](A)

Parameters

F

-

the domain of computation, a field

A

-

rectangular Matrix over values in F

Description

• 

NullSpace(A) returns a basis for the linear system A x = 0 over the field F as a set of Vectors B = {b1, b2, ...}.

• 

The (indexed) parameter F, which specifies the domain of computation, a field, must be a Maple table/module which has the following values/exports:

  

F[`0`]: a constant for the zero of the ring F

  

F[`1`]: a constant for the (multiplicative) identity of F

  

F[`+`]: a procedure for adding elements of F (nary)

  

F[`-`]: a procedure for negating and subtracting elements of F (unary and binary)

  

F[`*`]: a procedure for multiplying two elements of F (commutative)

  

F[`/`]: a procedure for dividing two elements of F

  

F[`=`]: a boolean procedure for testing if two elements in F are equal

Examples

withLinearAlgebra[Generic]:

Q`0`,Q`1`,Q`+`,Q`-`,Q`*`,Q`/`,Q`=`:=0,1,`+`,`-`,`*`,`/`,`=`

Q0,Q1,Q`+`,Q`-`,Q`*`,Q`/`,Q`=`:=0,1,`+`,`-`,`*`,`/`,`=`

(1)

A:=Matrix1,2,3,1,3,5,0,1,2

A:=123135012

(2)

NullSpaceQA

121

(3)

A:=Matrix1,2,3,2,4,6,1,2,3

A:=123246123

(4)

NullSpaceQA

210,301

(5)

See Also

LinearAlgebra[Generic], LinearAlgebra[Modular][Basis], LinearAlgebra[NullSpace], Nullspace


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